Later we will attempt to sort out whether or not there is a difference between a Shamrock and a Clover, but first another question, why are there both Shamrock bulbs and seeds available, and what's the difference?
The official "lucky" Irish plants go by the botanical name Trifoliium dubium and they are grown from tiny seeds. As you can see below, you can easily purchase authentic seeds that come from Ireland. They are small, and some are surprised by that, they expect a bigger package...if your expectations are realistic, you will be pleased with these easy to grow seeds.
For children and the young at heart, you might want to pick up a simple kit that comes with all you need, plants grow from the seeds in about a week.
They are very hardy plants, and just need to be kept watered. They won't last as long in a pot as they do grown outside in the right climate, but keep them in a place that gets some sun and keep them watered but not over-watered, and they should do just fine.
There is another nice flowering plant with MUCH larger heart shaped leaves that has the botanical name Oxalis deppei, and these plants are grown from bulbs. You will find an instructional video below on how to care for the bulb variety that some call a Shamrock, or I've seen some call it false-shamrock.
But to answer our question, the official lucky plants come from seeds.